The present invention is with respect to a cylinder for machines processing running lengths of material and, more specially to an impression cylinder for gravure printing presses or intaglio presses which, at its ends, is supported in an adjustable bearing frame and which has a pipe-like outer casing supported by self-aligning bearings at its ends, the casing having within it a core which is not turned and has an outer diameter smaller than the inner diameter of the casing, the casing being supported on the core by at least one support bearing which is coaxial to the casing and is symmetrical with respect to the middle of the casing.